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We present an algebraic method for solving the Bethe ansatz equations for the periodic totally asymmetric exclusion process (TASEP) with an arbitrary number of sites and particles. The Bethe ansatz equations are realized as an algebraic…

Mathematical Physics · Physics 2025-09-03 Shinsuke Iwao , Kohei Motegi

I study the technique of Algebraic Bethe Ansatz for solving integrable models and show how it works in detail on the simplest example of spin 1/2 XXX magnetic chain. Several other models are treated more superficially, only the specific…

High Energy Physics - Theory · Physics 2007-05-23 L. D. Faddeev

We present a unified algebraic Bethe ansatz for open vertex models which are associated with the non-exceptional $A^{(2)}_{2n},A^{(2)}_{2n-1},B^{(1)}_n,C^{(1)}_n,D^{(1)}_{n}$ Lie algebras. By the method, we solve these models with the…

High Energy Physics - Theory · Physics 2011-02-16 Guang-Liang Li , Kang-Jie Shi

In this note we construct Q-operators for the spin s open Heisenberg XXX chain with diagonal boundaries in the framework of the quantum inverse scattering method. Following the algebraic Bethe ansatz we diagonalise the introduced…

Mathematical Physics · Physics 2023-01-04 Rouven Frassek , István M. Szécsényi

By using the intertwiner and face-vertex correpondence relation, we obtain the Bethe ansatz equation of eight vertex model with open boundary condtitions in the framework of algebraic Bethe ansatz method. The open boundary condition under…

High Energy Physics - Theory · Physics 2010-01-15 Heng Fan , Bo-yu Hou , Kang-jie Shi , Zhong-xia Yang

In this work, we present a proof of the existence of real and ordered solutions to the generalized Bethe Ansatz equations for the one dimensional Hubbard model on a finite lattice, with periodic boundary conditions. The existence of a…

Strongly Correlated Electrons · Physics 2009-11-10 Pedro S. Goldbaum

This article is an interdisciplinary review and an on-going progress report over the last few years made by myself and collaborators in certain fundamental subjects on two major theoretic branches in mathematics and theoretical physics:…

Mathematical Physics · Physics 2007-05-23 Shi-shyr Roan

The exactly solvable four-vertex model on a square grid with the different boundary conditions is considered. The application of the Algebraic Bethe Ansatz method allows to calculate the partition function of the model. For the fixed…

Statistical Mechanics · Physics 2009-11-13 N. M. Bogoliubov

The Hofstadter problem is studied on hexagonal lattice. We first establish a relation between the spectra for the hexagonal lattice and for its dual he triangular lattice. Following the idea of Faddeev and Kashaev, we then obtain the…

Condensed Matter · Physics 2009-10-28 C. A. Piguet , D. F. Wang , C. Gruber

The Bethe ansatz represents an analytical method enabling the exact solution of numerous models in condensed matter physics and statistical mechanics. When a global symmetry is present, the trial wavefunctions of the Bethe ansatz consist of…

Quantum Physics · Physics 2024-05-24 Roberto Ruiz , Alejandro Sopena , Max Hunter Gordon , Germán Sierra , Esperanza López

In this work we diagonalize the double-row transfer matrix of the supersymmetric t-J model with non-diagonal boundary terms by means of the algebraic Bethe ansatz. The corresponding reflection equations are studied and two distinct classes…

Exactly Solvable and Integrable Systems · Physics 2009-11-13 W. Galleas

Using the Baxter's T-Q relation derived from the transfer matrix technique, we consider the diagonalization problem of discrete quantum pendulum and discrete quantum sine-Gordon Hamiltonian from the algebraic geometry aspect. For a finite…

High Energy Physics - Theory · Physics 2007-05-23 Shao-shiung Lin , Shi-shyr Roan

We describe a method to derive, from first principles, the long-distance asymptotic behavior of correlation functions of integrable models in the framework of the algebraic Bethe ansatz. We apply this approach to the longitudinal spin- spin…

Mathematical Physics · Physics 2009-09-25 N. Kitanine , K. K. Kozlowski , J. M. Maillet , N. A. Slavnov , V. Terras

We give a detailed description of the nested algebraic Bethe ansatz. We consider integrable models with a $\mathfrak{gl}_3$-invariant $R$-matrix as the basic example, however, we also describe possible generalizations. We give recursions…

Mathematical Physics · Physics 2020-09-02 N. A. Slavnov

By combining the algebraic Bethe ansatz and the off-diagonal Bethe ansatz, we investigate the supersymmetric t-J model with generic open boundaries. The eigenvalues of the transfer matrix are given in terms of an inhomogeneous T-Q relation,…

Mathematical Physics · Physics 2017-07-13 Pei Sun , Fakai Wen , Kun Hao , Junpeng Cao , Guang-Liang Li , Wen-Li Yang , Kangjie Shi

We have considered the Zamolodchikov-Fateev and the Izergin-Korepin models with diagonal reflection boundaries. In each case the eigenspectrum of the transfer matrix is determined by application of the algebraic Bethe Ansatz.

Exactly Solvable and Integrable Systems · Physics 2010-04-07 V. Kurak , A. Lima-Santos

We diagonalize the transfer matrix of a solvable vertex model constructed by combining the vector representation of U_q[Sl(n|m)] and its dual by means of the quantum inverse scattering framework. The algebraic Bethe ansatz solution consider…

Exactly Solvable and Integrable Systems · Physics 2008-11-26 G. A. P. Ribeiro , M. J. Martins

The XXZ Gaudin model with {\it generic} integerable boundaries specified by generic {\it non-diagonal} K-matrices is studied. The commuting families of Gaudin operators are diagonalized by the algebraic Bethe ansatz method. The eigenvalues…

High Energy Physics - Theory · Physics 2016-09-06 Wen-Li Yang , Yao-Zhong Zhang , Mark D. Gould

We present the exact solution of a family of fragmented Bose-Hubbard models and represent the models as graphs with the condensates in the vertices. The models are solved by the algebraic Bethe ansatz method. We show that the models have…

Exactly Solvable and Integrable Systems · Physics 2021-05-31 Gilberto N. Santos Filho

Motivated by Heilmann and Lieb's work, we discuss energy level crossings for the one-dimensional Hubbard model through the Bethe ansatz, constructing explicitly the degenerate eigenstates at the crossing points. After showing the existence…

Strongly Correlated Electrons · Physics 2009-11-10 Akinori Nishino , Tetsuo Deguchi